View source for Stochastic quantization

In [[Physics:Theoretical physics|theoretical physics]], '''stochastic quantization''' is a method for modelling quantum mechanics, introduced by [[Biography:Edward Nelson|Edward Nelson]] in 1966,<ref>{{Cite journal | last1 = Nelson | first1 = E. | title = Derivation of the Schrödinger Equation from Newtonian Mechanics | doi = 10.1103/PhysRev.150.1079 | journal = Physical Review | volume = 150 | issue = 4 | pages = 1079–1085 | year = 1966 |bibcode = 1966PhRv..150.1079N }}</ref><ref>{{Cite journal | last1 = Fényes | first1 = I. | doi = 10.1007/BF01338578 |bibcode=1952ZPhy..132...81F| title = Eine wahrscheinlichkeitstheoretische Begründung und Interpretation der Quantenmechanik| journal = Zeitschrift für Physik| volume = 132 | pages = 81–106| year = 1952 | issue = 1 | s2cid = 119581427 }}</ref><ref>{{Cite journal | last1 = De La Peña-Auerbach | first1 = L. |author-link1=Luis de la Peña| title = A simple derivation of the Schroedinger equation from the theory of Markoff processes | doi = 10.1016/0375-9601(67)90639-1 | journal = Physics Letters A | volume = 24 | issue = 11 | pages = 603–604 | year = 1967 |bibcode = 1967PhLA...24..603D }}</ref> and streamlined by  [[Biography:Giorgio Parisi|Parisi]] and Wu.<ref name="Parisi">{{cite journal|last = Parisi|first = G|year = 1981|title = Perturbation theory without gauge fixing|journal = Sci. Sinica|volume = 24|pages = 483|author2 = Y.-S. Wu}}</ref>
==Details==
Stochastic quantization serves to quantize Euclidean field theories,<ref name=damgaard>{{cite journal|last=Damgaard |first=Poul|author2=Helmuth Huffel |title=Stochastic Quantization |journal=Physics Reports|year=1987|volume=152|issue=5&6|pages=227–398|url=http://homepage.univie.ac.at/helmuth.hueffel/PhysRep.pdf|access-date=8 March 2013|bibcode = 1987PhR...152..227D |doi = 10.1016/0370-1573(87)90144-X |hdl=1721.1/3101|hdl-access=free}}</ref> and is used for numerical applications, such as numerical simulations of [[Physics:Gauge theory|gauge theories]] with [[Physics:Fermion|fermion]]s. This serves to address the problem of [[Physics:Fermion doubling|fermion doubling]] that usually occurs in these numerical calculations.

Stochastic quantization takes advantage of the fact that a Euclidean quantum field theory can be modeled as the [[Physics:Thermodynamic equilibrium|equilibrium limit]] of a [[Physics:Statistical mechanics|statistical mechanical system]] coupled to a [[Physics:Heat bath|heat bath]]. In particular, in the [[Physics:Path integral formulation|path integral]] representation of a Euclidean quantum field theory, the path integral measure is closely related to the [[Physics:Boltzmann distribution|Boltzmann distribution]] of a statistical mechanical system in equilibrium. In this relation, Euclidean Green's functions become [[Correlation function|correlation function]]s in the statistical mechanical system. A statistical mechanical system in equilibrium can be modeled, via the [[Ergodic hypothesis|ergodic hypothesis]], as the [[Stationary distribution|stationary distribution]] of a [[Stochastic process|stochastic process]]. Then the Euclidean path integral measure can also be thought of as the stationary distribution of a stochastic process; hence the name stochastic quantization.

== See also ==

* [[Physics:Supersymmetric theory of stochastic dynamics|Supersymmetric theory of stochastic dynamics]]
* [[Physics:Stochastic quantum mechanics|Stochastic quantum mechanics]]

==References==
{{reflist}}

[[Category:Stochastic processes]]



{{Sourceattribution|Stochastic quantization}}